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Absolute Value Inequalities - Problem 4 252 views

There are rules that you can memorize about whether the answer to an an absolute value inequality will involve an "and" or "or" compound inequality, but if you work carefully, you won't need to memorize them. Rather, isolate the absolute value expression, and split it into two inequalities. For the first, leave the inequality sign as it is and remove the absolute value signs. For the second, change the direction of the inequality sign, change the constant + - sign, and remove the absolute value signs. Solve each separately and graph them both on the same number line. If the graphs come together, then your solution is an "and," and if they go in opposite directions, then it's an "or" compound inequality.

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